On 01/04/2013 10:46 AM, JT wrote:> On 4 Jan, 15:46, JT<jonas.thornv...@gmail.com> wrote:>> I remember doing this in a tentamen during my education in information>> theory beleiving what i did was binary sort but my teacher informed me>> it wasn't so what is it.>> By creating a Pascal pointer binary tree with each leaf holding a>> integer, you move the binary numbers to the tree from least digit to>> highest using left legs for 0's and right for 1's. (Basicly creating>> leaves for new numbers, and at last digit you add 1 to the leaf slot.>> So after you moved all values into the tree and created all the nodes,>> you simply read out all the none zero values holded into the slot of>> the leaves within the binary tree.>>>> What is this sort called?>> Of course you cannot have more leaves then memory, but this does not>> need to hold memory for slots never used like the array slots, it is>> therefore my beleif that this sort could be useful also for database>> purposes sorting basicly anything. What do you think?>> I can see there would be problems reading out the sizes of a binary> tree from smallest to biggest, if you have legs with different> lengths? Is there any algorithmic solution to this problem.> I have kind of a foul play solution, you create a binary tree for> every digit bigger then 2^20 the smaller ones you run with the array> approach. So for 21,22,23... bits and so on each numbers run on their> own computers, with 2048 computers you could sort enormous amount of> data of different size. So basicly the "heaps?" all have legs with> same sizes and is easy to read out in order.> Is this a working idea or just plain silly, maybe it is just easier to> use one computer and read out the values from the heap and sort them> with quicksort after you filled up the tree? (Is it called tree or> heap, what is the difference betwee a heap and a tree?).>> So what you think about the mix using this kind of sort for counting> in values, and then quicksort to sort the none null tree nodes by> sizes.

Oops.. below is about factoring. The best algorithmshave been getting better since Maurice Kraitchik's [1920s]improvement on Fermat's method of expressing a numberas a difference of squares, n = a^2 - b^2, son = (a-b) (a+b).